Since "atheism" is simply "belief that no gods exist", there are a host of different reasons and motivations atheists can have for doing good deeds.
These are my reasons and motivations:
I believe that the Progress and Welfare of Humankind is the greatest good.
I believe that every human being has a Right to a minimally Decent life.
I believe that every human being wants to be Happy.
I'm moved by Compassion and Rational Self-Interest.
I could not Respect myself if I was cruel to others.
I cannot be Happy unless I try to shield others from suffering.
And, if I am Kind to others, I increase the chances they will be kind to me - making my life better, as well as theirs.
Therefore, I want to, and I try to, make the World a better place for everyone